Chaos最新文献

Camphor is a well-studied material capable of generating self-propelled motion at a water surface, and the resulting dynamics can exhibit a wide range of behaviors. Here, we analyze a one-dimensional model describing a mobile camphor disk perturbed by a second localized camphor source. The interaction between the rotor and the perturbing disk is represented by a distance-dependent potential. The study is motivated by experiments in which a camphor rotor interacts with a fixed camphor disk placed on the water surface. Numerical simulations of the model reproduce the essential features of the experimentally observed position-dependent rotor velocity for all considered forms of the potential. For weak perturbations, we derive analytical solutions valid for arbitrary potential profiles. Both the simulations and the analytical results demonstrate a pronounced asymmetry in the rotor velocity depending on whether the rotor approaches or recedes from the perturbation.

We investigate the occurrence of extremely large amplitude intermittent oscillations and transient dynamics in a silicon-based doubly clamped nanoelectromechanical system (NEMS) resonator driven by external periodic forcing. The system exhibits sudden, extensive amplitude variations induced by changes in the external periodic excitation. These large amplitude variations are characterized by analyzing the local maxima of the time series over an extended duration of time, up to the order of 106 normalized time units. The intermittent large amplitude oscillations satisfy the criteria for superextreme events and are further examined through their probability distribution functions. In addition, the peaks of intermittent oscillations that surpass a significant threshold are analyzed in terms of their inter-event intervals and total number of such events. Besides, the transient extreme events, arising under a different set of system parameters, are also studied, with their statistical distributions evaluated both with and without transients. Also, we included two-parameter phase diagrams to distinguish between regions associated with superextreme events and those exhibiting no such events. Further, we have also examined the effect of noise with varying control parameters. This study advances the understanding of unusual dynamical behaviors in NEMS resonators and underscores their potential relevance for future technological applications.

Extensive studies have been conducted on the activation mechanisms of game groups in complex networks characterized by pairwise interactions. However, these studies are insufficient to accurately capture the higher-order interaction scenarios in real-world systems. Therefore, we propose a continuous-strategy public goods game implemented on uniformly random hypergraphs, where the hyperedge activation function is determined by the hyperedge investment (denoted by α) and the baseline activation probability (denoted by β). Subsequently, the groups are categorized into three types (moderate, radical, and conservative) based on the value of the shape parameter δ in the hyperedge activation function. Additionally, the particle swarm optimization algorithm is adopted to update the strategies of agents. Simulation results demonstrate that the introduction of the hyperedge activation mechanism improves the cooperation level compared with the baseline model in which all hyperedges are consistently activated. Notably, when the group is radical, the cooperation level exhibits a non-monotonic relationship with the baseline activation probability β when reduced synergy factor r is small; when the group is conservative, the cooperation level demonstrates a non-monotonic relationship with the shape parameter δ at intermediate values of r. Moreover, we find that the individual learning weight in the particle swarm optimization algorithm exerts a non-monotonic influence on the cooperation level under certain parameter combinations.

We propose a coupled system for the nonlinear interaction between high-frequency, circularly polarized, intense electromagnetic (EM) waves and low-frequency electron-density perturbations, driven by the EM-wave ponderomotive force, in an unmagnetized plasma composed of fully degenerate relativistic electrons and stationary positive ions, including a higher-order correction to the nonlocal nonlinearity. We show that the modulational instability growth rate associated with the generation of EM envelope solitons is significantly reduced with a slight increase in either the nonlocal nonlinear correction or the degeneracy parameter. Furthermore, a three-wave temporal model predicts the existence of quasiperiodic and chaotic states of EM solitons while interacting with longitudinal electron-density perturbations. We show that the greater the degeneracy (or higher the contribution from the nonlocal correction), the smaller the instability domain of modulation wave numbers; thus, degeneracy favors the stability of EM soliton evolution. The existence of temporal chaos in a low-dimensional model could be a signature of the development of spatiotemporal chaos in the complete nonlinear model, in which many electromagnetic solitons can be excited and saturated as they interact with electron plasma waves.

Neuronal synchrony is a hallmark of both healthy and pathological brain dynamics, often regulated by delayed interactions and inhibitory control. In this study, we investigate how delayed inhibitory feedback-representing the collective action of a population of inhibitory neurons-modulates synchronization in an excitatory network of Hodgkin-Huxley neurons coupled via delayed conductance-based synapses. We find that the impact of such feedback depends strongly on the baseline network state. In synchronized network activity states and in transitional regimes at the border of synchrony and desynchrony, feedback with intermediate delays enhances synchrony, whereas in desynchronized activity states, the effect is minimal. Furthermore, a brief, strong external pulse can initiate network-wide synchrony, which is maintained only when inhibitory feedback is present. These findings demonstrate that population-level inhibitory feedback with delay can dynamically control network synchrony and induce bistable behavior, offering insight into mechanisms by which inhibitory circuits may stabilize or disrupt oscillatory activity in cortical networks.

Higher-order networks provide a powerful framework for modeling complex interaction dynamics that go beyond simple pairwise relationships. However, on the other hand, in many real-world scenarios, the underlying network topology is not directly observable, but only time-series data of node dynamics are available. The structure of higher-order networks is inherently more intricate than that of traditional pairwise networks. These make the accurate reconstruction of higher-order networks a critical challenge. Existing methods are typically limited by insufficient accuracy, and they overlook the inherent symmetry priors in undirected higher-order networks. To address this issue, we incorporate symmetry priors into the reconstruction process by embedding symmetric constraints into the iterative equation and the solving procedure by employing the block coordinate descent method. The proposed approach ensures reconstruction accuracy while reducing computational complexity. Theoretical analysis and numerical experiments show that our method achieves accuracy comparable to the conventional global method with efficiency close to the point-by-point method, providing a practical and scalable methodology for higher-order network reconstruction.

Clique percolation focuses on the connectivity of complete subgraphs rather than the local connectivity of edges or nodes, leading to distinct phase transition behaviors compared to traditional percolation models. Traditional simulation methods often require large system sizes and high computational costs, making them impractical for reliable results. This paper uses neural network methods to study the (k,l)-clique percolation phase transition on Moore lattices and Erdős-Rényi (ER) random networks. For Moore lattices, five methods were compared: (1) the 4N×N matrix-based convolutional neural network (CNN), (2) the 4N2×1 vector-based fully connected neural network (FCNN), (3) the largest cluster-based CNN, (4) the adjacency matrix-based CNN, and (5) the graph convolutional network (GCN). For ER random networks, two methods were used: (1) GCN based on edge connection and (2) the CNN with fixed nodes on a square lattice and random edge connections. The results show that (1) As k and l increase, identifying phase transition behavior becomes more difficult. (2) In Moore lattices, the 4N×N matrix-based CNN and the largest cluster-based CNN are effective methods. (3) For ER networks, GCN effectively identifies the (k,l)-clique percolation phase transition, while the fixed lattice CNN successfully detects the (2,1)-clique and (3,1)-clique transitions.

Invariant manifolds are fundamental geometric structures in the field of nonlinear dynamical systems, providing insights into the system's long-term global behavior. In the context of nondeterministic dynamical systems (e.g., stochastic or random dynamical systems), the concept of invariant manifolds generalizes but becomes more nuanced due to the presence of randomness or uncertainty and the definition of invariance must account for the probabilistic behavior. To address this concept, necessary definitions from the measurable dynamics' theory are introduced, including the flow map, the transfer operator and its dual in both closed and open spaces, and the classical Ulam discretization over the space of constant distributions along with its dual. Next, invariant manifolds for nondeterministic systems are defined, and a proof of existence is provided for a marginal distribution fWu over the unstable manifold, along with its dual observable gWs over the stable manifold. Finally, a discretization strategy for the open-flow transfer operator is presented, along with a method for computing fWu and gWs. In summary, the theory of measurable dynamics is employed to define and prove the existence of unstable manifold distributions and stable manifold observables via the spectrum of an open-flow transfer operator. In addition, a computational discretization procedure, based on the Ulam method, is introduced. The results of the electrically actuated microarch reveal three interconnected stochastic phenomena: diminished convergence probability, expansion of the stable manifold across its basin, and fusion of the unstable manifold with the attractor.

Housing policies greatly affect real estate markets, and the media quickly responds to the tone and consistency of housing policies. In this sense, news articles can be utilized to comprehend the relationship between market participants' reactions and housing policies. Based on daily news articles from three major media outlets covering the South Korean housing market, we employ the controlled growth process model to investigate the quantitative structure of news articles on housing policies and their association with embedded sentiment. Our findings reveal that word frequencies in news articles follow a power-law distribution, and a news article can be considered a semi-structured document in terms of the intermediate-level text cohesion between technical reports and narrative texts. Furthermore, differences in scaling exponents and text cohesion can explain the heterogeneous sentiment patterns of news articles on housing policies (i.e., the first- and second-order effects on sentiments in news articles). This study contributes to the existing literature by providing an extended window for understanding how linguistic patterns in word frequency distributions are interlinked with embedded sentiments. Regulators and policymakers can consider our theoretical framework for ex post policy evaluation, obtaining insights into scheming forward housing policies to relieve real estate markets. Investors can benchmark this analytical procedure in monitoring the housing market's responses to announced policies to adjust their strategies regarding real estate financing in a timely manner.

This paper presents a delayed viral infection model that incorporates cytokine enhancement, full logistic proliferation, and the cell-to-cell transmission pathway. The basic reproduction number, R0, is established as the threshold parameter determining viral clearance or persistence. By constructing suitable Lyapunov functionals and applying the M-matrix method, we establish the global asymptotic stability of both the infection-free and infected equilibria. Furthermore, sufficient conditions for the occurrence of a Hopf bifurcation at the infected equilibrium are derived, considering models with and without intracellular delay. Theoretical analysis reveals that a backward bifurcation occurs when the total death rate of infected cells falls below their proliferation rate. It is further shown that bistability does not arise under either complete therapeutic success (η=0) or complete failure (η=1). We find that ignoring the cytokine-enhanced effect may underestimate the basic reproduction number and the infection risk. Numerical simulations not only validate the theoretical findings but also uncover rich dynamics, including stability switches and chaotic oscillations. These results consistently demonstrate that higher therapeutic efficacy leads to reduced viral load. Finally, the combined impact of spatial diffusion and time delay on the infection dynamics is illustrated.